A method and apparatus for pumping a liquid

ABSTRACT

Embodiments relate to an electromagnetic, or electric, pump for pumping and/or transporting a liquid. Embodiments impart motion to a liquid, so as to stir, mix, circulate, or otherwise move the liquid. Embodiments transport water. The liquids can be conducting or non-conducting. Embodiments pump liquids in pipes. Embodiments utilize a shockwave effect, a magneto hydrodynamic effect, and/or an electrohydrodynamic effect to push the liquid. Embodiments operate with no mechanically moving parts, increasing the reliability of the pump. Embodiments of the electromagnetic (or electric) lifting, or pumping, device are thin such that the electrodes that create the pumping are installed inside the piping of the pump, reducing, or eliminating, sealing/leakage problems. Embodiments create one or more sparks, and/or filament discharges, triggered between one or more pairs of electrodes positioned such that a liquid is between the electrodes of the electrode pair, where the spark, or filament discharge, creates a plasma.

CROSS-REFERENCE TO RELATED APPLICATION

The present application claims the benefit of U.S. Provisional Application Ser. No. 61/738,307, filed Dec. 17, 2012, which is hereby incorporated by reference herein in its entirety, including any figures, tables, or drawings.

BACKGROUND OF INVENTION

There exists a need to transport liquid from remote and inaccessible locations in an efficient and reliable manner. As an example, in gas wells for oil/gas industry, mechanical pumps are used for de-watering applications, lifting hundreds of barrels of water per day (hundreds of cubic centimeters of water per second). The traditional way is expensive, and can be environmentally unsafe due to seal leakage issues with the pumps, and can also be plagued by fatigue and failure of the mechanical components. Accordingly, there is a need in the art for a liquid transportation method and apparatus that lowers the cost and reduces environmental harm with respect to mechanical pumps, while lifting the liquid with reasonable power at a reasonable recovery rate.

Underwater spark discharges were found and investigated for nearly a century [1] and have been employed in various applications. Examples include underwater acoustic source in deep ocean oil prospecting [2] and minesweeping applications [3], underwater plasma source in advanced water sterilization method [4,5], powerful underwater shock wave source in extracorporeal lithotripsy [6] and oil well dredging [7], and active reaction source in water treatment [8,9]. In recent decades, many relative experiments [10,11,12,13,14] had been designed for understanding the mechanism of this complex physical phenomenon. Based on these experiment results some theoretical and empirical models [15,16,17,18,19] have also been developed to predict the shock wave pressure, electro-acoustical efficiency, chemical reaction, ionization, and associated plasma processes.

BRIEF SUMMARY

Embodiments of the invention relate to an electromagnetic, or electric, pump for pumping and/or transporting a liquid. Additional embodiments can be used for imparting motion to a liquid, so as to, for example, stir, mix, circulate, or otherwise move the liquid. Specific embodiments relate to transporting water. Even though much of the description is directed to specific embodiments for transporting water, the description also applies to embodiments for transporting other liquids and to imparting motion to a liquid. The liquids can be conducting or non-conducting. Specific embodiments can be referred to as a plasma liquid pump and are designed for pumping liquids in pipes. Specific embodiments of the pumps can operate with no mechanically moving parts, increasing the reliability of the pump. Embodiments of the subject electromagnetic (or electric) lifting, or pumping, device can be thin such that the electrodes that create the pumping can be installed inside the piping of the pump, reducing, or eliminating, sealing/leakage problems. Embodiments of the invention create one or more sparks, and/or filament discharges, triggered between one or more pairs of electrodes positioned such that a liquid is between the electrodes of the electrode pair, where the spark, or filament discharge, creates a plasma.

With a plasma caused by a spark, the energy of the plasma is released locally in the water or other liquid, causing vaporization of the water or other liquid. The vaporized water then creates a vapor bubble that creates a compressional acoustic wave, or shockwave. The shockwave then pushes the water or other liquid. By positioning the one or more electrode pairs that creates the shockwave in a desired position with respect to an appropriately designed structure, the direction the shockwave pushes the water can be controlled. Embodiments utilize thermodynamic effects to pump the liquid, such as water, where the pump moves the liquid by utilizing the liquid phase change, i.e., vaporization, and thermal expansion of the vapor, i.e., a bubble, that creates a shockwave. Specific embodiments can create such shockwaves for imparting motion to a liquid, so as to, for example, stir, mix, circulate, or otherwise move the liquid. The shockwave generated can also be used to clean the pipe or other structure in which the shockwave is generated.

Further embodiments incorporate a magneto hydrodynamic (MHD) effect, which can be utilized underwater, or under other liquids. Such an MHD effect can be created by using a filament discharge to create a plasma that creates ionized particles that are moving in a magnetic field such that the magnetic field imparts a force on the ionized particles. The force the magnetic field imparts on the ionized particles creates a force that imparts motion to the liquid. Specific embodiments relate to a pump that utilizes the magneto hydrodynamic effect to pump water, or other liquid. Embodiments can use a MHD effect for imparting motion to a liquid, so as to, for example, stir, mix, circulate, or otherwise move the liquid.

Further embodiments incorporate an electrohydrodynamic (EHD) effect, which can be utilized underwater, or under other liquids. Embodiments can create a plasma between the electrodes of one or more electrode pairs and the plasma creates an EHD force by ionized particles being pushed by an electric field, such as the electric field created by the one or more pairs of electrodes. The EHD force then imparts motion to the liquid. Specific embodiments relate to a pump that utilizes the EHD effect to pump water or other liquid. Specific embodiments can use an EHD effect for imparting motion to a liquid, so as to, for example, stir, mix, circulate, or otherwise move the liquid.

BRIEF DESCRIPTION OF DRAWINGS

FIG. 1 shows a spark discharge generating circuit that can be utilized with a specific embodiment of the subject invention.

FIG. 2 shows a one-direction valve that can be implemented in accordance with the invention.

FIG. 3 shows a pair of point-shaped electrodes.

FIG. 4 shows a schematic of a water jet measurement setup that can be used to measure how much water or other liquid is pushed by the spark.

FIG. 5 shows a water jet created by a spark created via an embodiment of the subject invention.

FIG. 6 shows a voltage measured via an oscilloscope during a spark that causes a shockwave in an embodiment of the invention.

FIG. 7 shows a section view of an embodiment of a pump having a self-generated magnetic field pump (SGMP) design.

FIG. 8 shows a side view of the SGMP design pump of FIG. 7.

FIG. 9 shows a section view of an embodiment incorporating an applied magnetic field pump (AMP) design.

FIG. 10 shows a side view of the AMP design pump of FIG. 9.

FIG. 11 shows a circuit of an experiment setup, A is A/C power source, T is transformer, D is diode, C is the capacitor, G is spark gap switch, S is safety resistance, and E is the underwater spark.

FIG. 12 shows the electrical potential and electric field in experiment setup (symmetric).

FIGS. 13A-13C show comparisons of bubble radius, wall velocity, and pressure, respectively.

FIGS. 14A-14C show comparisons of input power, temperature, and radiation power, respectively.

FIGS. 15A-15C show comparisons of radiation energy, internal energy, and mechanical energy, respectively.

FIGS. 16A-16C show comparisons of bubble radius, wall velocity, and pressure, respectively.

FIGS. 17A-17C show comparisons of input power, temperature, and radiation power, respectively.

FIGS. 18A-18C show comparisons of radiation energy, internal energy, and mechanical energy, respectively.

FIG. 19 shows an embodiment of a pump incorporating a shockwave effect.

FIG. 20 shows an embodiment of a pump incorporating a magneto hydrodynamic (MHD) effect.

FIG. 21 shows an embodiment of a pump incorporating an electrohydrodynamic (EHD) effect.

FIG. 22 shows a power supply for a deep pump.

FIG. 23 shows a multistage design, where 3 positions are available for the pump section.

DETAILED DISCLOSURE

Embodiments of the invention relate to an electromagnetic, or electric, pump for pumping and/or transporting a liquid. Additional embodiments can be used for imparting motion to a liquid, so as to, for example, stir, mix, circulate, or otherwise move the liquid. Specific embodiments relate to transporting water. Even though much of the description is directed to specific embodiments for transporting water, the description also applies to embodiments for transporting other liquids and to imparting motion to a liquid. Specific embodiments can be referred to as a plasma liquid pump and are designed for pumping liquids in pipes. Specific embodiments of the pumps can operate with no mechanically moving parts, increasing the reliability of the pump. Embodiments of the subject electromagnetic (or electric) lifting, or pumping, device can be thin such that the electrodes that create the pumping can be installed inside the piping of the pump, reducing, or eliminating, sealing/leakage problems. Embodiments of the invention create one or more sparks, and/or filament discharges, triggered between one or more pairs of electrodes positioned such that a liquid is between the electrodes of the electrode pair, where the spark, or filament discharge, creates a plasma.

With a plasma caused by a spark, the energy of the plasma is released locally in the water or other liquid, causing vaporization of the water or other liquid. The vaporized water then creates a vapor bubble that creates a compressional acoustic wave, or shockwave. The shockwave then pushes the water or other liquid. By positioning the one or more electrode pairs that creates the shockwave in a desired position with respect to an appropriately designed structure, the direction the shockwave pushes the water can be controlled. Embodiments utilize thermodynamic effects to pump the liquid, such as water, where the pump moves the liquid by utilizing the liquid phase change, i.e., vaporization, and thermal expansion of the vapor, i.e., a bubble, that creates a shockwave. Specific embodiments can create such shockwaves for imparting motion to a liquid, so as to, for example, stir, mix, circulate, or otherwise move the liquid. The shockwave generated can also be used to clean the pipe or other structure in which the shockwave is generated.

Embodiments can employ underwater, or other liquid, plasma discharge to push water, or other liquid, in the desired direction. FIG. 1 shows a circuit that can be utilized with an embodiment of the subject liquid pump. Capacitor (C) is charged to a high voltage by a circuit includes a transformer (T) and a diode (D). When the spark gap switch (B) is triggered, an electrical spark discharge is generated between the two underwater electrodes (Z). Then the energy released locally heats the fluid within the gap between the two electrodes (Z). This leads to an instantaneous vaporization of the water, or other liquid, and also creates a plasma. A vapor bubble is launched, creating an acoustic wave in all directions. This underwater shockwave then pushes the water or other liquid. In a specific embodiment, the acoustic wave is a spherical acoustic wave.

Referring to FIG. 1, after capacitor is charged, an electrical spark is generated between electrodes due to high voltage. During the spark, the energy released locally heats the water positioned in the gap between the electrodes. This release of energy that heats the water leads to an instantaneous vaporization of the water, followed by thermal expansion of the vapor in a vapor bubble. An acoustic wave, e.g., a spherical acoustic wave, is created which drives the water. Embodiments can have internal structures that are shaped such that, in combination with electrode pairs positioned appropriately with respect to the internal structures push the water in the desired direction. Specific embodiments can utilize piping or other conduits, which can have a variety of cross-sectional shapes, such as circular, elliptical, rectangular, polygonal, or other shape that enhances the pumping effect on the liquid. FIG. 2 shows an embodiment with a parabolic surface to reflect the acoustic wave generated by the underwater spark discharge. The parabolic structure can be located, for example, on the bottom of a small tube or at a portion of the internal pipe structure that then directs the shockwave to drive the water or other liquid within the pump. The underwater electrodes can be placed on the focus point of the paraboloid, such that the shockwave can be reflected in a manner symmetric with the internal structure and, in a parallel fashion. In addition, a one-direction valve can be positioned on the bottom of the paraboloid, letting the water come into the tube while preventing the water from leaving the tube.

In a specific embodiment, the design can have an oblique arrangement. As shown in FIG. 2, the tube is located around the wall of the pipe so that it requires less force to pump the water. The underwater discharge electrodes can have a variety of shapes that allow the generation of a shockwave. Electrode pairs can have one electrode on or proximate the inner surface of the pipe and another electrode offset from the first electrode, in a direction having a component along the direction of travel of the liquid, in a direction having a component perpendicular to the direction of travel of the liquid, and/or in a direction having a component away from the liquid. FIG. 3 shows a pair of electrodes that can be used with an embodiment of the invention. Two point-shaped electrodes shown in FIG. 3, by having pointed electrode ends, enhance the electrical field around the point which makes the discharge easier to ignite. Electrodes having a variety of pointedness can be used.

Tests were conducted with respect to an embodiment of the invention. In order to measure the voltage for the discharge, a high voltage probe was employed with an oscilloscope. The trigger mode was used, and the voltage curve for the spark discharge was recorded. In accordance with specific embodiments, during bubble and shockwave generation, there are three main stages in the liquid, which can be referred to as the beginning phase, vaporization, and thermal expansion. In a specific embodiment, for moving water via shockwave, the water has a temperature of 20° C. and a pressure of 101 kPa prior to creating the spark. The enthalpy of water is 84 kJ/kg. Prior to vaporization, the pressure is presumed to be constant. The saturation point is 100° C. and 101 kPa, so the vapor created has enthalpy of 2680 kJ/kg.

A constant volume can be assumed, since the bubble will not collapse at this stage. The highest pressure assumed to be reached is about 500 kPa. The enthalpy of this superheated vapor is 6000 kJ/kg. If the energy input via the electrodes is ˜100 J, the radius of the bubble, r, can be solved for via the following equation:

${\frac{4}{3}\pi \; r^{3}} = {\frac{100\mspace{14mu} J}{\left( {6000 - 84} \right)\frac{KJ}{kg}}1700\mspace{14mu} {cm}^{3}\text{/}g}$ r = 1.9  cm d = 3.8  cm

A specific embodiment relates to a water jet. The water jet, a schematic of which is shown in FIG. 4, can allow a measurement of how much water one pulse (i.e., one spark) can push, and then investigate how much energy is needed for this and other pump designs. Before the spark, the water level and the top of the curved tube are even. After the spark, the water in the device is the water pushed by the spark up to this level.

FIG. 5 shows a photo at the moment of an underwater spark discharge. The photo shows that a water jet is pushed by the discharge out of the tube. FIG. 6 shows a voltage curve measured from the oscilloscope, with current and power curves calculated according to the capacitor (30 μF, 4 kV). The voltage curve shows damping after the spark. However, it is reported the critical damping will happen with saline water [Ref. 1]. Moreover, the calculated current curve is up to ˜7000 Amps while the discharge. Table 1 shows the data observed from the water jet measurement setup, which shows the amount of water pushed by the spark with different voltage, along with the 95% confidence interval to indicate the data reliability. From the data, the water jet increases as the voltage increases. However, lower voltages have higher efficiency. The results indicate that the bubble size can be reduced while maintaining the pipe at the same size, the size of the pipe can be increased while maintaining the size of the bubbles, or the size of the pipe can be increased and the size of the bubbles reduced, in order to enhance performance. Further, increasing the voltage can reduce the amount of energy needed to generate the spark.

TABLE 1 Water pushed by single millisecond pulse of various voltages Voltage Energy Water Pushed Standard 95% Confidence (kV) (J) (Mean) (g) Deviation Interval (g) 2.2 72.6 17.7 1.6 14.6 20.7 3.1 144.2 21.4 1.7 18.1 24.7 3.5 183.8 23.5 1.2 21.2 25.9

For a required flow rate of 100 bbls per day=184 cm3/s=˜184 g/s, four pumps can be employed in a staggered configuration along the pipe wall, so as to lift water in a peristaltic manner. In an embodiment, water can be pumped at a rate of 70 g of water per pulse of 2.2 kV. By controlling the trigger signal on the spark gap switch to be 3 cycles per second the pump can be operated in a duty cycle. An embodiment can pump 210 g/s of water (i.e., approximately 114 bbls/day). The average power consumption for such an embodiment is estimated based on the collected data to be less than 1 kW. A variety of designs can be implemented in accordance with embodiments of the invention, including, but not limited to, electrodes having pointed, flat, cylindrical, or other shapes, electrodes with electrode spacing (distance between electrodes) of 0.1 mm to 50 mm, applied voltage duty cycle for applying voltage to create spark to the electrode pair of 1 millimeter to 1 kilohertz, an applied voltage range of 1 kV to 100 kV, electrode material comprising tungsten, copper, aluminum, carbon nanotubes, steel, or other metal that can bear high energy, cross-sectional areas in the range of 1 square mm to 1 square meter, liquids to be pumped such as water, oil, dielectric liquids, electrically conductive liquids, biological fluids, and other liquids that can be pumped via shockwaves, voltage and electrode spacings that result in electric fields creates by the applied voltage in the range of 10⁵ V/m to 10⁸ V/m, and liquids to be pumped having pressures in the range of 100 pascals to 10⁸ pascals, 1 mbar to 500 bar, and/or 1 bar to 200 bar. A specific embodiment utilizes a linear combination of the device of FIG. 2 such that each device of FIG. 2 pumps the water or other liquid to the next such device and the liquid is transported along the linear combination. The device shown in FIG. 2 can also be combined in parallel to increase the volume of liquid being transported.

A specific embodiment can have electrodes extend out from near the sides and create the spark at or near the center of the pump such that the flow of the liquid is at or near the center of the pump.

FIG. 19 shows a longitudinal cross-section of a pump utilizing a shock wave effect. The electrodes are positioned in a concave portion of a parabolic reflector such that the shockwave is guided to push the liquid in the identified (arrows) flow regions. Various designs can be implemented. In a specific embodiment, the section of pump shown in FIG. 19 can be positioned in one of the locations, or other location, shown in FIG. 23, of a segment of a pump, where each segment of the pump via, for example, a one way valve that allows the liquid to be pumped through the valve in one direction and prevents (or reduces) flow of the liquid in the other direction.

Embodiments using a shockwave effect to pump a liquid can have a variety of shapes, sizes, and operating conditions. Specific embodiments can utilize a spark discharge, created by voltages in the range 1 kV to 100 kV, a cross-sectional area in the range of 6 cm² to 400 cm² (e.g., diameter in the range 2.5 cm to 20 cm), pulse duration in the range 1 ms to 10 ms, and stage height in the range 1 m to 30 m.

Further embodiments incorporate a magneto hydrodynamic (MHD) effect, which can be utilized underwater, or under other liquids. Such an MHD effect can be created by using a filament discharge to create a plasma that creates ionized particles that are moving in a magnetic field such that the magnetic field imparts a force on the ionized particles. The force the magnetic field imparts on the ionized particles creates a force that imparts motion to the liquid. Specific embodiments relate to a pump that utilizes the magneto hydrodynamic effect to pump water, or other liquid. Embodiments can use a MHD effect for imparting motion to a liquid, so as to, for example, stir, mix, circulate, or otherwise move the liquid.

The magnetic field can be generated using one or more of the electrodes that is used to generate the filament discharge or can be supplied independent of such electrodes. An embodiment incorporating a self-generated magnetic field pump (SGMP) design incorporating an MHD effect. FIG. 7 shows an embodiment that utilizes a self-generated magnetic field. In the embodiment of a SGMP design pump shown in FIG. 7, one rod electrode in the center of the tube and one sheet of plate electrode surrounding the tube surface are used to generate an underwater discharge. The filament discharge is generated between the rod electrode and tube wall with the discharge current being in the radial direction, while the current in the rod electrode, shown by the large arrow in the electrode, generates an annular magnetic field, B. The Lorentz's force, F, resulting from the discharge current, i, and self-generated magnetic field, B, is toward the outlet of the tube. The current I in the rod electrode and the generated magnetic field B can both be reversed at the same time and the pump will pump in the same direction. If either the rod electrode current I or the magnetic field B, but not the other, is reversed, the pump will push in the opposite direction. The cross-sectional shape of the tube can be rectangle, triangle, or other desired shape.

A specific embodiment can utilize an applied magnetic field pump (AMP) design. FIG. 9 shows an embodiment using an AMP design pump, which is similar to the SGMP design in that the embodiment shown in FIG. 9 also uses discharge current and magnetic field to generate a Lorentz's force to push the fluid. However, the magnetic field in this embodiment is generated by several electromagnets. The use of electromagnets allows larger magnetic fields, and, therefore, larger Lorentz's forces. Electromagnets can also be placed outside the tube. FIG. 10 shows a cross-section of the pump of FIG. 9. Other methods of creating the magnetic field can also be utilized, such as the use of magnetics or a combination of magnets, current, and electromagnets. The cross-sectional shape of the tube can be rectangle, triangle, or other desired shape.

FIG. 20 shows an embodiment of a pump using an MHD effect, which has a different structure for creating the discharge current (via electric field E) and a different structure for creating the magnetic field B. The electrodes are plate electrodes on opposite sides of a rectangular cross-section and the magnets (electromagnets or other magnets) create a B field perpendicular (or having a component that is perpendicular) to the E field created by the electrode. In this way the force on the liquid is into or out of page, depending on the direction of the discharge current and B field. Many other structures for creating the E field and B field can be implemented.

Embodiments using a MHD effect to pump a liquid can have a variety of shapes, sizes, and operating conditions. Specific embodiments can utilize a filament discharge, created by voltages in the range <500V for the rod electrode and 1 kV to 30 kV for the plate electrode, a cross-sectional area in the range of 0.25 cm² to 400 cm² (e.g., diameter in the range 0.5 cm to 20 cm), pulse duration in the range 1 μs to 1 ms, and stage height in the range 10 cm to 10 m. Specific embodiments can have the rod current and the discharge current on and off at the same time and have a rod voltage to discharge voltage in the range 1:10 to 1:10,000; 1:10 to 1:100; 1:100 to 1:1,000; or 1:100 to 1:10,000.

Further embodiments incorporate an electrohydrodynamic (EHD) effect, which can be utilized underwater, or under other liquids. Embodiments can create a plasma between the electrodes of one or more electrode pairs and the plasma creates an EHD force by ionized particles being pushed by an electric field, such as the electric field created by the one or more pairs of electrodes. The EHD force then imparts motion to the liquid. Specific embodiments relate to a pump that utilizes the EHD effect to pump water or other liquid. Specific embodiments can use an EHD effect for imparting motion to a liquid, so as to, for example, stir, mix, circulate, or otherwise move the liquid.

A specific embodiment can have electrodes extend out from near the sides and create the spark at or near the center of the pump such that the flow of the liquid is at or near the center of the pump.

FIG. 21 shows an embodiment incorporating an EHD effect. A voltage is applied across the electrodes and a spark or a filament discharge is created that creates a plasma and the ionized particles created by the plasma are pushed by the E-field between the two electrodes, such that the fluid between the two electrodes is pushed.

FIG. 22 shows a power supply that can be used for a pump using a shockwave effect, an MHD effect, and/or an EHD effect. The magnetic power mount is not needed for the shockwave effect or the EHD effect.

FIG. 23 shows how a pump can be divided into segments and the segments interconnected by one-way valves such that flow can go in one direction and is prevented or reduced in the other direction. The pump section(s) in FIG. 23 can be one or more of a pump using a shockwave effect, an MHD effect, and/or an EHD effect. Pumps using any of a shockwave effect, an MHD effect, and/or an EHD effect can have a design that spirals the liquid that reduces the force needed to transport the liquid.

Embodiments using an EHD effect to pump a liquid can have a variety of shapes, sizes, and operating conditions. Specific embodiments can utilize a spark discharge or filament discharge, created by voltages in the range 1 kV to 100 kV, a cross-sectional area in the range of 0.25 cm² to 400 cm² (e.g., diameter in the range 0.5 cm to 20 cm), pulse duration in the range 100 μs to 10 ms, and stage height in the range 10 cm to 30 m.

Sparks and filament discharge generated for various embodiments of the subject invention can be created by applying a voltage across two electrodes with a liquid positioned between the two electrodes and a spark discharge will be discussed. For discussion, water will be used as the liquid between the two electrodes. The spark discharge can be brief, such as on the order of a few microseconds. The brief mechanism of underwater spark discharge can be divided into two parts. At the beginning of the first part, when the capacitor, charged with a high voltage, is connected to the discharge circuit, a high electric field (E>MV/m) is formed in the liquid channel between the two submerged electrodes. Immediately after, in a non-conducting liquid such as pure water, a low density channel is formed between the electrodes due to electrostatic repulsion and electrostriction force [11], an electrical spark discharge initiates within this channel due to high E-field. In a conducting liquid like sea water, this high electric field generates a large current that goes directly through the liquid and forms an evaporation channel in it. During the second part, which is the same for both conducting and non-conducting liquids, the energy stored in the capacitor is released violently through the channel and the Joule heating effect evaporates the liquid, followed by dissociation and ionization [6]. Consequently, the channel with high pressure and temperature expands rapidly in all directions as a spherical bubble. This bubble wall eventually starts oscillating due to the water compressibility generating sequential spherical acoustic compression waves. In summary, the first part of this process is bubble initiation due to high electric field, and the second part is pulsed energy release and bubble expansion and oscillation. Thus, the bubble characteristics are mainly determined from the second part.

For underwater spark discharges used in conducting liquids, such as sea water, the salinity of water, which affects the conductivity, influences the rate of energy release in the water, and thus effects the bubble growth.

Theoretical simulations of the bubble generated by underwater spark discharge have been performed using a circuit model with salinity and large ambient pressure effects.

2. Theoretical Analysis 2.1 Assumptions

The following assumptions are made for the theoretical model: (1) The bubble is a symmetric sphere. (2) The effects of gravity are negligible. (3) The pressure and temperature inside the bubble are uniformly distributed. (4) The compressibility of water only affects the outside of the bubble. (5) Thermal effects of water are negligible outside the bubble. (6) The plasma inside the bubble is in local thermal equilibrium (LTE).

Assumption (1)-(3) are made to simplify the problem to a zero dimensional (0-D) model. Assumption (4) is made due to the fact that the bubble generated by spark discharge grows with a high wall velocity (>transonic). Consequently, thermal conduction in this fast process can be neglected [20], which is assumption (5). Finally, assumption (6) is made according to the plasma parameters obtained in the experiment [15]. The temperature and electron density of plasma inside the bubble can reach up to eV and 10²⁸ m⁻³, respectively, for which, the lifecycle of the plasma is several milliseconds. In order to be considered as LTE plasma, this transient plasma must fulfill two criteria [21]:

$\begin{matrix} {{N_{e} \geq {10^{23}\left( \frac{kT}{E_{H}} \right)^{1/2}{\left( \frac{E_{2} - E_{1}}{E_{H}} \right)^{3}\left\lbrack m^{- 3} \right\rbrack}}},} & (1) \\ {{\tau \approx {\frac{1.15 \times 10^{7}N^{+}}{f_{21}{N_{e}\left( {N^{+} + N} \right)}}\left( \frac{E_{2} - E_{1}}{E_{H}} \right)\left( \frac{kT}{E_{H}} \right)^{1/2}{{\exp \left( \frac{E_{2} - E_{1}}{kT} \right)}\left\lbrack \sec \right\rbrack}}},} & (2) \end{matrix}$

where N_(e) is the electron density, k is the Boltzmann constant, T is temperature, E_(H) is the first ionization energy of hydrogen (or oxygen) atom, E_(n) is the nth electron state energy, τ is the relaxation time, f₂₁ is the absorption oscillator strength, N⁺ and N are the number density of ions and neutral atoms, respectively. In [21] it was shown that for this plasma N_(e)≧10²⁴ m⁻³ and τ<10⁻⁹ s which satisfy the LTE criteria from Eqs. (1) and (2).

2.2 Bubble Model

We used an effective model published by Lu et al. [15] with some modification to simulate the bubble variation. According to the assumptions listed above, the 0-D bubble model of underwater spark discharge should consider water compressibility and neglect thermal effects on the surrounding water. So, the Kirkwood-Bethe approximation of bubble equation of motion, as an effective model, is employed to simulate bubble oscillation process,

$\begin{matrix} {{{\left( {1 - {\frac{1}{C}\frac{R}{t}}} \right)R\frac{^{2}R}{t^{2}}} + {\frac{3}{2}\left( {1 - {\frac{1}{3}\frac{1}{C}\frac{R}{t}}} \right)\left( \frac{R}{t} \right)^{2}}} = {{\left( {1 + {\frac{1}{C}\frac{R}{t}}} \right)H} + {\left( {1 - {\frac{1}{C}\frac{R}{t}}} \right)\frac{R}{C}{\frac{H}{t}.}}}} & (3) \end{matrix}$

In Eq. (3), H, the specific enthalpy, and C, the speed of sound, are the properties of liquid attaching the bubble, and R is the radius of the bubble. Since thermal effects are neglected in the water outside the bubble, explicit expressions for C and H can be derived by using the modified Tait equation of state [22]:

$\begin{matrix} {{\frac{p + B}{p_{\infty} + B} = \left( \frac{\rho}{\rho_{\infty}} \right)^{n}},} & (4) \end{matrix}$

where p and ρ are the pressure and density of liquid attaching the bubble, ρ_(∞) and ρ_(∞) represent the pressure and density of water in the undisturbed region far from the bubble. The constants B=3.04913×10⁸ Pa, n=7.15, are based on reasonable matching with the experimental pressure-density relation of water in the pressure range up to 10 GPa [22].

Since the bubble wall is an interface of water and vapor, there is a difference between pressures on both sides of the wall due to normal stresses, which is

$\begin{matrix} {{p_{B}(t)} = {{p_{i}(t)} - {\frac{1}{R}{\left( {{2\sigma} + {4\mu \frac{R}{t}}} \right).}}}} & (5) \end{matrix}$

Here p_(B)(t) and p_(i)(t) are the pressures on the liquid side and vapor side of the interface, respectively, a is the liquid-vapor surface tension, and μ is the viscosity of the liquid. However, the pressure difference caused by surface tension and liquid viscosity is much less than the internal pressure generated by spark discharge. So, this difference can be neglected and p is used to represent the pressure on both sides of the bubble wall.

Spark discharges use less energy than arc discharge, and only produce transitory conductive channels that bridge the gap between the electrodes [10]. Bubble pressure can be calculated using ideal gas model with contributions from all particles inside the bubble,

$\begin{matrix} {{p = \frac{{kTN}\; {\eta \left( {N,V,T} \right)}}{V}},} & (6) \end{matrix}$

where k is the Boltzmann constant, T is the temperature of plasma, N is the number of equivalent whole water molecules in the bubble, η(N, V, T) is the ratio of the number of all particle species to N (such that Nη is the total particle number in the bubble), and V is the bubble volume which is expressed by the bubble radius R.

In order to derive the expression for temperature, T, the time derivative of the internal energy is needed.

$\begin{matrix} {{\frac{E}{t} = {{\left( \frac{\partial E}{\partial N} \right)_{V,T}\frac{N}{t}} + {\left( \frac{\partial E}{\partial V} \right)_{N,T}\frac{V}{t}} + {\left( \frac{\partial E}{\partial T} \right)_{N,V}\frac{T}{t}}}},} & (7) \end{matrix}$

Since the bubble here is an open system, a different expression for the energy balance with energy flow can be derived from the first law of thermodynamics,

$\begin{matrix} {{\frac{E}{t} = {q - {p\frac{V}{t}} + {\left( \frac{\partial E}{\partial N} \right)_{V,T}\frac{N}{t}}}},} & (8) \end{matrix}$ q=q _(input)−(1−γ)q _(rad) −q _(m),  (9)

where q_(input) is the energy flow injected in the spark between the electrodes from circuit, q_(rad) is the heat flow due to radiation, γ is the fraction of the radiant energy absorbed by the bubble interface for evaporation, q_(m) is the energy flow that includes evaporation, condensation and heating due to the mass exchange through the interface.

By combining Eqs. (7) and (8), the expression for T is

$\begin{matrix} {{\left( \frac{\partial E}{\partial T} \right)_{N,V}\frac{T}{t}} = {q - {\left\lbrack {p + \left( \frac{\partial E}{\partial V} \right)_{N,T}} \right\rbrack {\frac{V}{t}.}}}} & (10) \end{matrix}$

In order to derive the expression of internal energy, E, needed for solving Eq. (10), the analysis of the internal content of the bubble should be predetermined. Inside the bubble, we can simply consider reactions due to high temperature and pressure, dissociation of water molecules into separated atoms and ionization of hydrogen and oxygen atoms. Since assumed that the plasma inside bubble is in LTE, the dissociation and ionization processes must be in equilibrium. For such an equilibrium, let S be the probability of the state that gas of i species with N_(i) particles has in a given volume, V. The probability for dissociation is

$\begin{matrix} {{S = {{\prod_{i}\frac{Z_{i}^{N_{i}}}{N_{i}!}} = {\frac{Z_{H}^{N_{H}}}{N_{H}!}\frac{Z_{O}^{N_{O}}}{N_{O}!}\frac{Z_{H_{2}O}^{N_{H_{2}O}}}{N_{H_{2}O}!}}}},} & (11) \end{matrix}$

where Z_(i) is the partition functions for each particle species i. For hydrogen and oxygen atoms, the expression is

$\begin{matrix} {{Z_{i} = {g_{i}{V\left( \frac{2\pi \; m_{i}{kT}}{h^{2}} \right)}^{3/2}}},} & (12) \end{matrix}$

where h is the Planck constant, g_(i) is the degeneracies of the particle t and m_(i) is the mass of the particle i. The partition functions for water molecules are identical, except there the binding energy, D, is included.

$\begin{matrix} {Z_{H_{2}O} = {g_{H_{2}O}{V\left( \frac{2\pi \; m_{H_{2}O}{kT}}{h^{2}} \right)}^{3/2}{{\exp \left( \frac{D}{kT} \right)}.}}} & (13) \end{matrix}$

From dissociation of N water molecules, we have

N _(H)=2N _(O),  (14)

N _(H) ₂ _(O) =N−N _(O).  (15)

Then, taking the derivative of the natural log of Eq. (11) and using Stirling's approximation for N, N_(i)>>1, we can get the dissociation equilibrium expression

$\begin{matrix} {{\frac{\left( {\ln \; S} \right)}{N_{O}} = {{{2\ln \; Z_{H}} + {\ln \; Z_{O}} - {\ln \; Z_{H_{2}O}} - {2{\ln \left( N_{H} \right)}} - {\ln \; N_{O}} + {\ln \left( N_{H_{2}O} \right)}} = 0}},} & (16) \\ {\frac{N_{H}^{2}N_{O}}{N_{H_{2}O}} = {\frac{Z_{H}^{2}Z_{O}}{Z_{H_{2}O}} = {\frac{V^{2}g_{H}^{2}g_{O}}{g_{H_{2}O}}\left( \frac{m_{O}}{m_{H_{2}O}} \right)^{3/2}\left( \frac{2\pi \; m_{H}{kT}}{h^{2}} \right)^{3}{{\exp \left( {- \frac{D_{H_{2}O}}{kT}} \right)}.}}}} & (17) \end{matrix}$

For ionization equilibrium, the ionization potential is the same for both hydrogen oxygen atoms. So, only the ionization equilibrium equation of the hydrogen atom is calculated for both atom ionization processes,

$\begin{matrix} {{\frac{N_{H^{+}}N_{e}}{N_{H}} = {\frac{{Vg}_{H^{+}}g_{e}}{g_{H}}\left( \frac{m_{H^{+}}}{m_{H}} \right)^{3/2}\left( \frac{2\pi \; m_{e}{kT}}{h^{2}} \right)^{3/2}{\exp \left( {- \frac{I_{1}}{kT}} \right)}}},} & (18) \end{matrix}$

where I₁ is the first ionization potential of hydrogen (or oxygen) atom. Now the internal energy, E, can be derived from Eq. (17) and (18) as

E=N[(1−α₁)∈_(H) ₂ _(O)+α₁ D+3α₁(1+α₂)∈+3α₁α₂ I ₁],  (19)

where α₁ and α₂ are the degree of dissociation and the degree of ionization which can be easily calculated from equilibrium equations, and ∈_(H) ₂ _(O)=3 kT and ∈=3/2 kT are internal energies for water molecule and all other particle species, respectively. The particle-molecule ratio, η, can be expressed as,

η(N,V,T)=1+2α₁+3α₁α₂.  (20)

Due to high equilibrium temperature, the thermal radiation also needs to be considered in spark discharge plasmas. Here, we used blackbody assumption for the bubble surface,

q _(rad)=4πR ²σ_(r) T ⁴.  (21)

where σ_(r) is the Stefan-Boltzmann constant.

Mass exchange at the bubble wall plays a very important role as bubble properties vary. According to gas dynamic theory [23] and radiant evaporation, the mass flow rate of water, {dot over (m)}, and corresponding energy flow rate, q_(m), can be expressed as,

$\begin{matrix} {{\overset{.}{m} = {{\frac{4\pi \; R^{2}\alpha_{M}}{\sqrt{2\pi \; R_{v}}}\left( {\frac{p^{*}}{\sqrt{T_{l}}} - {\Gamma \; \frac{p}{\sqrt{T}}}} \right)} + \frac{\gamma \; g_{{ra}\; d}}{{c_{l}\left( {T_{p\; h} + T_{l}} \right)} + l}}},} & (22) \end{matrix}$ q _(m) ={dot over (m)}(c ₁(T _(ph) −T _(l))+l+∫ _(T) _(ph) ^(T) c _(p)(T′)dT′).  (23)

In Eq. (22), the first term is due to gas dynamic, where α_(M) is the accommodation coefficient for evaporation or condensation (assumed constant), equal to the ratio of vapor molecules sticking to the phase interface to those impinging on it, p is the actual vapor pressure, p* is the equilibrium vapor pressure, T and T_(l) are the temperatures of the vapor and the liquid at the phase interface respectively, and R_(V) is the gas constant of the vapor. The deviation of the velocity distribution from a Maxwellian distribution is described by the factor Γ, which is equal to unity for equilibrium conditions [22]. Second term is radiant evaporation mass flow, where T_(ph) is the phase change temperature of water, c_(l) is the liquid specific heat capacity at constant pressure, and l is the latent heat of evaporation or condensation. In Eq. (23), c_(p)(T) is the vapor specific heat capacity at constant pressure. The equilibrium vapor pressure can be calculated from Clausius-Clapeyron equation as [22]:

$\begin{matrix} {{p^{*} = {p_{c}{\exp \left\lbrack {\frac{L}{R_{v}T_{c}}\left( {1 - \frac{T_{c}}{T_{l}}} \right)} \right\rbrack}}},} & (24) \end{matrix}$

where T_(c) and p_(c) are the temperature and pressure at the critical point, for water 647.096 K and 2.206×10⁷ Pa [22], respectively. The specific heat at constant pressure can be expressed as,

$\begin{matrix} {{c_{p}(T)} = {{\frac{1}{{Nm}_{H_{2}O}}\left( \frac{\partial E}{\partial T} \right)_{N,V}} + {R_{v}.}}} & (25) \end{matrix}$

Note, the time derivative of water molecule number can be expressed as,

$\begin{matrix} {\frac{N}{t} = {\frac{\overset{.}{m}}{m_{H_{2}O}}.}} & (26) \end{matrix}$

2.3 Circuit Model

The circuit of the power system is shown FIG. 11. This circuit includes two separate function section, charging section and discharging section, sharing a capacitor. In the beginning of each pulse cycle, power source charges the capacitor to high voltage via transformer in the charging section. When spark gap switch is triggered, a high energy pulse is generated from discharging the capacitor and ignite underwater spark between two underwater electrodes. Then bubble is generated and oscillated as described.

During the discharging period, the bubble of plasma can be simply treated as a resistor. Thus, the discharging section becomes a series RLC circuit. So, we can use series RLC model to simulate this section,

$\begin{matrix} {{{L\; \frac{i}{t}} + {R_{total}i} + {\frac{1}{C}{\int_{t_{0}}^{t}{i{t^{\prime}}}}} - {V_{C}\left( t_{0} \right)}} = 0.} & (27) \end{matrix}$

In Eq. (27), L is the inductance of this section, R_(total) is the total resistance in this section, including both circuit resistance R_(c) and gap resistance R_(g), a is the current, C is the capacitance, V_(C) represents the voltage on the capacitor. If we consider the resistance is constant during the discharge, the circuit becomes a simple series RLC circuit with analytical solution,

i(t)=A ₁ e ^(s) ¹ ^(t) +A ₂ e ^(s) ² ^(t)  (28)

where A_(1,2) are constant, and

$\begin{matrix} {{s_{1,2} = {{- \alpha} \pm \sqrt{\alpha^{2} - \omega_{0}^{2}}}},{\alpha = \frac{R_{total}}{2L}},{\omega_{0} = \frac{1}{\sqrt{LC}}}} & (29) \end{matrix}$

Note, knowing the capacitance and measuring the current for the circuit allows one to fit a model to find resistance and inductance. Also, the input power can be determined as,

q _(input) =i ² R _(g).  (30)

Since two resistors are the only power consumption components in the circuit model, the total energy input into the water gap is,

$\begin{matrix} {E_{input} = {\frac{R_{g}}{R_{g} + R_{c}}{\frac{{{CV}_{C}\left( t_{0} \right)}^{2}}{2}.}}} & (31) \end{matrix}$

3. Results 3.1 Salinity

Salinity influences the electrical conductivity of the liquid, and thus very important in the electrical breakdown of water and the subsequent thermal and hydrodynamic phenomena. The ratio of electrical permittivity to conductivity in liquid, ∈_(l)/σ_(l), i.e. the Maxwell relaxation time, is the time scale which characterizes the charge relaxation due to Ohmic conduction, and for a very short energy pulse relative to this relaxation time the fluid behaves as a dielectric [10].

Bourlion et al. [6] presented voltage and current curves for both pure and saline water conditions. They used sodium chloride aqueous solution with concentration of 100 g/l, which can be convert to electrical conductivity of 14.29 S/m. For pure water discharge, after a random latency period, under-damped discharge ignites to high oscillating current. In saline water case, current curve is aperiodic, which indicates that the discharge is close to critically damped. Based on given capacitance and initial voltage, the resistance can be fitted from Eqs. (28) and (29). The total resistance for pure water gap is 260 mΩ and that for saline water is 1000 mΩ. Although the resistance of the gap during discharge is varying, the constant resistance calculated from fitting is in good agreement according to statistics of the fitting.

Poison's equation s solved according to the geometry of the experimental setup. The results of electrical potential and electrical field are shown in FIG. 2. Then, the equivalent resistance of the saline water can be calculated by:

$\begin{matrix} {{R_{g} = \frac{V_{g}}{I_{g}}},{{{where}\mspace{14mu} I_{g}} = {\int_{0}^{R}{\sigma_{s}{E_{field}\left( {2\pi \; r} \right)}{{r}.}}}}} & (32) \end{matrix}$

Here, V_(g)=1 V denotes voltage applied between two electrodes, I_(g) is the current pass through the gap, is the saline water conductivity and the integration is along the Y=α line. For saline water case described above, the gap resistance is calculated as 1500 mΩ. The possible reason of the difference between the calculated and the fitted values is due to the drop in resistance of the channel caused by evaporation and ionization during the first part of the discharge process.

The increase in gap resistance for saline water can be also explained by the mechanism in the first part of underwater spark. For dielectric liquid, such as pure water, high electric field caused by capacitor discharge generates electrostatic repulsion and electrostriction force creating a low density liquid channel [11]. Therefore, a random latency period [6] may appear in this case due to the channel formation process. Electrical discharge initiated in the channel evaporates and then ionizes the liquid into plasma, which become a low conductivity channel for releasing stored energy. For conductive liquid, this high electric field directly moves charged particles in the liquid to release energy bypassing the formation of a low density channel. Subsequently, the liquid evaporates, and eventually ionizes, due to Joule heating. Thus, relatively higher resistance in this case can be explained as heavier charged particles in comparison with the case of pure water (dielectric liquid). Furthermore, it can be foreseen that there must be a threshold condition connects these two typical cases describe above.

3.2 Simulation results

Five different cases are numerically simulated for studying the underlying influences of salinity and pressure. For numerical simulations of all cases, initial conditions and parameters are selected and validated according to experimental work [15].

$\begin{matrix} {{p_{ini} = {2p_{\infty}}},{T_{ini} = {400\mspace{14mu} K}},{\frac{R}{t} = {6\mspace{14mu} m\text{/}s}},} & (33) \end{matrix}$ γ=0.2,α_(m)=10⁻⁴.  (34)

Based on the experimental setup [6], the following circuit parameters are utilized:

C=100 nF,L=100 nH,V _(C)(t ₀)=13.5 kV,R _(c)=50 mΩ.  (35)

The water properties for all cases are listed in Tab. 1. The gap resistances for unsalted water and salted water case are calculated from fitted value. While the gap resistance for all sea water cases is calculated from the conductivity ratio between themselves and salted case. The sea water salinities and temperatures are the average values.

TABLE 1 Water properties for all cases [24] Temper- Ambient Conduc- Gap Salinity ature Pressure Density tivity Resistance (g/l) (° C.) (Pa) (kg/m³) (S/m) (mΩ) Unsalted N/A 20 1.01 × 10⁵  998.21 N/A  210 Water Salted 100 20 1.01 × 10⁵ 1074.05 14.29  950 Water Sea Water  35 20 1.01 × 10⁵ 1024.75 4.79 2835 (Average) Deep Sea  35 10   5 × 10⁶ 1029.32 3.81 3564 (500 m) Deep Sea  35  5   1 × 10⁷ 1032.38 3.35 4056 (1000 m) 3.2.1 Salinity analysis

For salinity analysis, all properties during bubble expansion and oscillation process of all atmospheric cases are plotted together for comparison in FIGS. 13A-13C, 14A-14C, and 15A-15C. In order to compare the differences, the time axis of each case is plotted in logarithmic scale and is normalized according to the first bubble oscillation cycle period. And the cycle periods of all 3 cases are shown in the legend of FIG. 13A in parenthesis. Note that the first cycle period for unsalted case does not include the random latency period.

Comparison of bubble radii is plotted in FIG. 13A. As shown in the legend, the first bubble cycle periods are 325 ms, 3.35 ms and 3.37 ms for unsalted, salted and sea water cases, respectively. All 3 cycle periods are close to each other. Similarly, the maximum radii for unsalted (1.76 cm), salted (1.75 cm) and sea water (1.81 cm) cases are also very close. Furthermore, after first expansion, the bubble shrinks to a smaller size due to liquid compressibility. Although the bubble radii are almost identical for all 3 cases, the maximum wall velocities of 3 bubbles shown in FIG. 13B are varies with large differences. Case with higher gap resistance tends to have higher and earlier wall velocity in the beginning stage of the discharge. Furthermore, the trend of wall velocity is the same as that of pressure shown in FIG. 13C. The velocity of bubble wall is in the transonic range of water and the pressure is in GPa level. Combination of the velocity and pressure, the spark discharge bubble can generate powerful acoustic wave.

FIG. 14A shows the instantaneously input power to the bubble from the circuit. This property is decided purely by the circuit parameters. The periodic decreasing curve of unsalted case implies under-damped discharge; larger aperiodic curve of salted case indicates critical damped discharge; wider aperiodic curve of sea water case indicates over-damped discharge. Moreover, FIG. 14A also shows that the maximum input power of salted case is the largest among 3 cases. Temperature comparison plotted in FIG. 14B shows sudden increase for all 3 cases. And the trend of temperature is also that case with higher gap resistance tends to have higher and earlier temperature increase. As shown in Eq. (21), radiation power is a function of temperature and bubble surface area, the curves in FIG. 4( c) show combined trends from them.

FIGS. 15A-15C shows energy distribution during the first bubble cycle. Radiation energy curves plotted in FIG. 15A calculated by integrate radiation power along time. It shows that the salted case lost less energy via radiation than other 2 cases. The internal energy (shown in FIG. 15B) difference in the beginning stage is due to the different input power curve. Since the similar energy distribute into radiation loss and internal energy, the differences on mechanical energy is mainly due to the different amount of energy inputted into the gap.

The difference among atmospheric cases can be explained as follows: since the gap resistances are different among 3 cases, the total input energy can be calculated as 7.36 J (unsalted) 8.66 J (salted) and 8.96 J (sea water) according to Eq. (31). Additionally, it is known that the circuit is under-damped in unsalted case, almost critical damped in salt case and over-damped in sea water case. These differences lead to the fact that the input power of unsalted case is smaller but last periodically, the input power of salted case is higher and more intense and the input power of sea water case starts earlier and last longer without periodic features. The earlier input power will be just used to heat smaller amount of particles in a smaller bubble, which results with higher temperature and pressure in sea water case. However, intense temperature peak in early stage emits less radiation energy due to smaller bubble surface area in salted case. Meanwhile, high pressure inside the bubble does more mechanical work during bubble expansion process in both salted and sea water cases. Since the internal energy and radiation energy are about the same at the end of first cycle, mechanical energy differences are mainly due to the difference of energy inputted to the water gap described by Eq. (31).

3.2.2 Ambient Pressure Analysis

Furthermore, different ambient pressure is also analyzed by simulating seawater spark discharge in different depth. FIGS. 16A-16C, 17A-17C, and 18A-18C shows the comparisons of all properties for all cases in sea water. Similarly, the time axis of each case is plotted in logarithmic scale and is normalized according to the first bubble oscillation cycle period. And the cycle periods of all 3 cases are shown in the legend of FIG. 16A in parenthesis.

FIG. 16A shows the comparison of radii for all sea water cases. It shows that the deeper the case locates, the smaller the bubble can expend and the shorter the first bubble cycle can last. Furthermore, apart from the radii comparison, all other 8 properties plotted in FIGS. 16A-16C, 17A-17C, and 18A-18C just show simple shifts in the time fraction axis among 3 cases.

The comparison between different ambient pressure cases indicates that large ambient pressure prevents the vapor bubble from expanding to larger radius due to thermodynamic relations of pressure, temperature, and specific volume. This results in a smaller first bubble cycle. Accordingly, bubble properties like temperature, pressure, and system energy of deep ocean cases do not develop as quickly as in the atmospheric case.

The numerical analysis of the bubble formation and oscillation processes created by underwater spark discharge in different salinity and different ambient pressure conditions and the experimentally validated bubble growth model used for the bubble simulations showed periodic oscillation of bubbles, as the bubble grew in size its boundary become unstable causing random collapse during the process. This explains why there was no second bubble cycle detected in some cases. Analysis of the different energy releasing mechanisms in conductive and dielectric liquids demonstrated that gap resistance in the circuit is a key difference between underwater sparks in dielectric liquid and in conductive liquid. In dielectric liquid (pure water), stored energy releases through low resistance plasma channel formed by electrostatic repulsion and electrostriction force after a random latency period. In conductive liquid (salted water and sea water), stored energy releases directly through the current driven by high electric field in the liquid which results in higher resistance. Furthermore, the gap resistance influences total energy release into the liquid and its damping characteristics. Specifically in conductive liquid, the larger total input energy for a single intense pulse shaped input power generates higher temperature, higher pressure and higher bubble wall velocity. Therefore, more mechanical energy is released to surrounding liquid in comparison with dielectric liquid case. Hence, bubble generated by spark discharge in conductive liquid has larger pressure, no latency period, and does more mechanical work with the same energy consumed. Simulation of spark discharge generation in deep ocean conditions at 500 m and 1000 m deep sea water, indicates smaller bubble radii and shorter bubble cycles in comparison with atmospheric sea water case, while maximum pressures and maximum temperatures in both cases are almost the same, respectively. Thus, less mechanical work is done in this case. However, similar pressure and wall velocity in both saline water cases suggest the underwater spark is functional even in deep ocean condition.

Aspects of the invention may be described in the general context of computer-executable instructions, such as program modules, being executed by a computer. Generally, program modules include routines, programs, objects, components, data structures, etc., that perform particular tasks or implement particular abstract data types. Moreover, those skilled in the art will appreciate that the invention may be practiced with a variety of computer-system configurations, including multiprocessor systems, microprocessor-based or programmable-consumer electronics, minicomputers, mainframe computers, and the like. Any number of computer-systems and computer networks are acceptable for use with the present invention.

Specific hardware devices, programming languages, components, processes, protocols, and numerous details including operating environments and the like are set forth to provide a thorough understanding of the present invention. In other instances, structures, devices, and processes are shown in block-diagram form, rather than in detail, to avoid obscuring the present invention. But an ordinary-skilled artisan would understand that the present invention may be practiced without these specific details. Computer systems, servers, work stations, and other machines may be connected to one another across a communication medium including, for example, a network or networks.

As one skilled in the art will appreciate, embodiments of the present invention may be embodied as, among other things: a method, system, or computer-program product. Accordingly, the embodiments may take the form of a hardware embodiment, a software embodiment, or an embodiment combining software and hardware. In an embodiment, the present invention takes the form of a computer-program product that includes computer-useable instructions embodied on one or more computer-readable media.

Computer-readable media include both volatile and nonvolatile media, removable and nonremovable media, and contemplate media readable by a database, a switch, and various other network devices. By way of example, and not limitation, computer-readable media comprise media implemented in any method or technology for storing information. Examples of stored information include computer-useable instructions, data structures, program modules, and other data representations. Media examples include, but are not limited to, information-delivery media, RAM, ROM, EEPROM, flash memory or other memory technology, CD-ROM, digital versatile discs (DVD), holographic media or other optical disc storage, magnetic cassettes, magnetic tape, magnetic disk storage, and other magnetic storage devices. These technologies can store data momentarily, temporarily, or permanently.

The invention may be practiced in distributed-computing environments where tasks are performed by remote-processing devices that are linked through a communications network. In a distributed-computing environment, program modules may be located in both local and remote computer-storage media including memory storage devices. The computer-useable instructions form an interface to allow a computer to react according to a source of input. The instructions cooperate with other code segments to initiate a variety of tasks in response to data received in conjunction with the source of the received data.

The present invention may be practiced in a network environment such as a communications network. Such networks are widely used to connect various types of network elements, such as routers, servers, gateways, and so forth. Further, the invention may be practiced in a multi-network environment having various, connected public and/or private networks.

Communication between network elements may be wireless or wireline (wired). As will be appreciated by those skilled in the art, communication networks may take several different forms and may use several different communication protocols. And the present invention is not limited by the forms and communication protocols described herein.

All patents, patent applications, provisional applications, and publications referred to or cited herein are incorporated by reference in their entirety, including all figures and tables, to the extent they are not inconsistent with the explicit teachings of this specification.

It should be understood that the examples and embodiments described herein are for illustrative purposes only and that various modifications or changes in light thereof will be suggested to persons skilled in the art and are to be included within the spirit and purview of this application.

REFERENCES

-   [1] Hulburt E O 1924 Physical Review 24 129-33 -   [2] Cannelli G, D'Ottavi E and Prosperetti A 1990 Oceans '90     (Washington, D.C.) 533-7 -   [3] Fry L H, Adair J P and Williams R 1999 12th IEEE International     Pulsed Power Conference (Monterey, Calif.) 2 781 -   [4] Clements J S, Sato M and Davis R H 1987 IEEE Transactions     Industry Applications 23 224 -   [5] Willberg D M, Lang P S, Hochemer R H, Kratel A and Hoffmann M R     1996 Environmental Science & Technology 30 2526-34 -   [6] Bourlion M, Dancer P, Lacoste F, Mestas J L and Cathignol D 1994     Review of Scientific Instruments 65 2356-63 -   [7] Zhao H, Lan A, Zhang J and Wang Z 1998 Oilfield Chemistry 15 113     (in Chinese) -   [8] Cho Y I, Lane J and Kim W 2005 International Communications in     Heat and Mass Transfer 32 861-71 -   [9] Yang Y, Kim H, Starikovskiy A, Fridman A and Cho Y I 2010 Water     Research 44 3659-68 -   [10] Locke B R and Thagard S M 2012 Plasma Chemistry and Plasma     Processing 32 875-917 -   [11] Starikovskiy A 2013 Plasma Sources Science & Technology 22 5 -   [12] Sankin G N, Simmons W N, Zhu S L and Zhong P 2005 Physical     Review Letters 95 4 -   [13] Obreschkow D, Kobel P, Dorsaz N, de Bosset A, Nicollier C and     Farhat M 2006 Physical Review Letters 97 4 -   [14] Ando K, Liu A Q and Ohl C D 2012 Physical Review Letters 109 5 -   [15] Lu X P, Pan Y, Liu K F, Liu M H and Zhang H J 2002 Journal of     Applied Physics 91 24-31 -   [16] Grinenko A, Gurovich V T, Saypin A, Efimov S, Krasik Y E and     Oreshkin V I 2005 Physical Review E 72 7 -   [17] Skoro N, Marie D, Malovic G, Graham W G and Petrovic Z L 2011     Physical Review E 84 4 -   [18] Buogo S, Plocek J and Vokurka K 2009 Acta Acustica United with     Acustica 95 46-59 -   [19] Cook J A, Gleeson A M, Roberts R M and Rogers R L 1997 Journal     of the Acoustical Society of America 101 1908-20 -   [20] Plesset M S and Prosperetti A 1977 Annual Review of Fluid     Mechanics 9 145-85 -   [21] Griem H R 1963 Physical Review 131 1170 -   [22] Prosperetti A and Lezzi A 1986 Journal of Fluid Mechanics 168     457-78 -   [23] Fujikawa S and Akamatsu T 1980 Journal of Fluid Mechanics 97     481 -   [24] 1962 The Sea vol 1, ed Hill M N (New York: WEILY) 

1. A device for pushing a liquid, comprising: at least one pair of electrodes, wherein each pair of electrodes of the at least one pair of electrodes comprises a corresponding first electrode of a corresponding at least one first electrode and a corresponding second electrode of a corresponding at least one second electrode; and an electric charge source, wherein the electric charge source is controllably electrically connected to the at least one pair of electrodes such that when the electric charge source is electrically connected to the at least one pair of electrodes when the at least one pair of electrodes are in contact with a liquid positioned between the first electrode and the second electrode of each pair of electrodes of the at least one pair of electrodes, a corresponding at least one spark is produced across the at least one pair of electrodes, wherein each spark of the at least one spark vaporizes a corresponding portion of the liquid of a corresponding at least one portion of the liquid, so as to produce a corresponding at least one shockwave, wherein the at least one shockwave pushes the liquid.
 2. The device according to claim 1, wherein the device further comprises: a structure, wherein the structure holds a volume of the liquid, wherein the at least one pair of electrodes is positioned with respect to the structure such that the at least one pair of electrodes are in contact with the liquid positioned between the first electrode and the second electrode of each pair of electrodes of the at least one pair of electrodes.
 3. The device according to claim 2, wherein the structure is a tube, wherein the at least one shockwave pushes the liquid such that some of the liquid is transported from a first portion of the pipe to a second portion of the pipe.
 4. The device according to claim 1, wherein the electric charge source is electrically connected to the at least one pair of electrodes in accordance with a duty cycle such that a repetition of sparks is produced across each pair of electrodes of the at least one pair of electrodes.
 5. The device according to claim 1, wherein the electric charge source provides a voltage in the range 1 kV to 100 kV.
 6. The device according to claim 2, wherein the tube has a cross-sectional area in the range 6 cm² to 400 cm².
 7. The device according to claim 5, wherein the voltage is pulsed with pulses having a duration in the range 1 ms to 10 ms.
 8. The device according to claim 2, wherein the structure has a plurality of segments, wherein adjacent segments of the plurality of segments are separated by a corresponding one-way valve such that the fluid is pushed through the corresponding one-way valve in a corresponding first direction and flow of the fluid is prevented or at least partially restricted in a corresponding second direction through the one-way valve.
 9. The device according to claim 8, wherein each segment of the plurality of segments has a height in the range 1 m to 30 m, wherein height is measured in a direction of flow of the fluid within the corresponding segment.
 10. The device according to claim 2, wherein the device is a pump, wherein when the pump is oriented in a first orientation the pump pumps the liquid up from a first vertical position to a second vertical position, wherein the second vertical position is higher than the first vertical position.
 11. A device for pushing a liquid, comprising: at least one pair of electrodes, wherein each pair of electrodes of the at least one pair of electrodes comprises a corresponding first electrode of a corresponding at least one first electrode and a corresponding second electrode of a corresponding at least one second electrode; a magnetic field source, wherein the magnetic field source produces a magnetic field; and an electric charge source, wherein the electric charge source is controllably electrically connected to the at least one pair of electrodes such that when the electric charge source is electrically connected to the at least one pair of electrodes when the at least one pair of electrodes are in contact with a liquid positioned between the first electrode and the second electrode of each pair of electrodes of the at least one pair of electrodes, a corresponding at least one discharge current is produced across the at least one pair of electrodes such that each discharge current of the at least one discharge current has a corresponding component that is perpendicular to the magnetic field, wherein each discharge current of the at least one discharge current creates charged particles that move in the magnetic field such that the magnetic field imparts a corresponding at least one Lorentz force on the charged particles, wherein the at least one Lorentz force imparted on the charged particles pushes the liquid. 12-20. (canceled)
 21. A device for pushing a liquid, comprising: at least one pair of electrodes, wherein each pair of electrodes of the at least one pair of electrodes comprises a corresponding first electrode of a corresponding at least one first electrode and a corresponding second electrode of a corresponding at least one second electrode; and an electric charge source, wherein the electric charge source is controllably electrically connected to the at least one pair of electrodes such that when the electric charge source is electrically connected to the at least one pair of electrodes when the at least one pair of electrodes are in contact with a liquid positioned between the first electrode and the second electrode of each pair of electrodes of the at least one pair of electrodes, (i) a corresponding at least one spark or a corresponding at least one filament discharge is produced across the at least one pair of electrodes, (ii) each spark of the at least one spark or each filament discharge of the at least one filament discharge creates a corresponding plasma of a corresponding at least one plasma, and (iii) a corresponding at least one electrohydrodynamic force is produced, wherein the at least one electrohydrodynamic force pushes the liquid. 22-30. (canceled)
 31. The device according to claim 1, wherein energy from the at least one spark heats the liquid, such that the at least one portion of the liquid is vaporized, wherein vaporization of the at least one portion of the liquid creates a corresponding at least one vapor bubble that creates a corresponding at least one acoustic wave, wherein the at least one acoustic wave is the at least one shockwave.
 32. The device according to claim 1, further comprising: a second at least one pair of electrodes, wherein each pair of electrodes of the second at least one pair of electrodes comprises a corresponding first electrode of a corresponding at least one first electrode and a corresponding second electrode of a corresponding at least one second electrode; and a second electric charge source, wherein the second electric charge source is controllably electrically connected to the second at least one pair of electrodes such that when the second electric charge source is electrically connected to the second at least one pair of electrodes when the second at least one pair of electrodes are in contact with the liquid positioned between the first electrode and the second electrode of each pair of electrodes of the second at least one pair of electrodes, (i) a corresponding second at least one spark or a corresponding second at least one filament discharge is produced across the second at least one pair of electrodes, (ii) each spark of the second at least one spark or each filament discharge of the second at least one filament discharge creates a corresponding plasma of a corresponding at least one plasma, and (iii) a corresponding second at least one electrohydrodynamic force is produced, wherein the second at least one electrohydrodynamic force pushes the liquid.
 33. The device according to claim 32, wherein the second at least one spark or of the second at least one filament discharge creates ionized particles, wherein the at least one electrohydrodynamic force is caused by the ionized particles being pushed by a corresponding at least one electric field created by the second electric charge source being electrically connected to the second at least one pair of electrodes.
 34. The device according to claim 1, further comprising: a second at least one pair of electrodes, wherein each pair of electrodes of the second at least one pair of electrodes comprises a corresponding first electrode of a corresponding at least one first electrode and a corresponding second electrode of a corresponding at least one second electrode; a magnetic field source, wherein the magnetic field source produces a magnetic field; and a second electric charge source, wherein the second electric charge source is controllably electrically connected to the second at least one pair of electrodes such that when the second electric charge source is electrically connected to the second at least one pair of electrodes when the second at least one pair of electrodes are in contact with the liquid positioned between the first electrode and the second electrode of each pair of electrodes of the second at least one pair of electrodes, a corresponding at least one discharge current is produced across the second at least one pair of electrodes such that each discharge current of the at least one discharge current has a corresponding component that is perpendicular to the magnetic field, wherein the at least one discharge current creates charged particles that move in the magnetic field such that the magnetic field imparts a corresponding at least one Lorentz force on the charged particles, wherein the at least one Lorentz force imparted on the charged particles pushes the liquid.
 35. The device according to claim 2, wherein the at least one shockwave stirs, mixes, and/or circulates the liquid.
 36. The device according to claim 2, wherein the structure comprises a paraboloid portion, wherein a first pair of electrodes of the at least one pair of electrodes is positioned at a focus point of the paraboloid portion.
 37. The device according to claim 2, wherein the structure comprises a parabolic reflector, wherein a first pair of electrodes of the at least one pair of electrodes is positioned in a concave portion of the parabolic reflector.
 38. The device according to claim 37, wherein the structure further comprises a guide section, wherein liquid reflected by the parabolic reflector is guided by the guide section. 